Three articles on broken edreform in the USA

Below are three articles summarizing many viewpoints I believe about education in the USA.

Each is very well written and together they share the central themes that teaching is a profession and a fundamental sea change is needed in policy and in public perception for anything to get better in the USA.  Business models of "carrot and stick" dangerously oversimplify a very complex and human problem by pretending human beings are simply commodities produced by factories (schools).  These oversimplifications have no backing when experience and "data" is analysed and they come with disastrous results for our students and ultimately our nation.


http://smokingtowardnewjersey.blogspot.com/2013/05/education-is-none-of-our-business.html
"
The fundamental problem is the business paradigm itself.  It is a model that will not do for education, because it assumes a whole range of things about education that are simply untrue or unacceptable: that kids’ circumstances outside of school do not influence them in school; that test scores are accurate reflections of achievement; that competition always produces the desired outcome; that opening and closing schools is as easy or advisable as opening and closing stores; that uniformity is not only possible, but good; that money is the best motivation for workers; and on and on.

[...]

The plain fact is, no business model, no matter how distorted, works for education because education is a complex human system involving a web of interrelationships, not a thing that’s created and traded on a supply chain. Some aspects of education may indeed be measurable in limited ways, but to assume that you have a clear picture of the whole endeavor based on those measures is foolhardy in the extreme. Beyond that, education is something we as a society have deemed a right, not a commodity. Rights are non-negotiable, never to be bought and sold on the open market.
"
and

http://goodmenproject.com/education-2/hesaid-i-have-only-one-thing-to-say-to-jeff-bliss-the-kids-who-criticized-his-teacher-on-youtube/

"
I have recently been criticized for my blogs and people have argued that I am not a social worker, but a history teacher, and that, by being a nurturer first, I am doing my students a disservice in school and life. I, and my former students and my colleagues throughout the world, would overwhelmingly disagree with their argument. All teachers are social workers first because we are dealing with social beings. In a perfect world, where every student comes from a loving and supportive home and feels confident and secure, teachers wouldn’t have to be as concerned with focusing on a student’s social needs, but that’s not realistic. Even I, who had a very loving and supportive family, still needed the love and support of my kindergarten teacher to help build my confidence and security when I was at a very insecure and awkward age.

[...]

If anything, this incredible speech by this amazing young man is exactly why, as a nation, we have to allow teachers to focus more on developing and nurturing young minds instead of taking the human relationship out of the equation by forcing teachers to not care about a child as a person, but solely as a test score. In my eight years as a teacher, I have had dozens of former students contact me after graduation and not a single one of them contacted me to thank me for helping them prepare for standardized tests, but to thank me for preparing them for life and for caring about them when they were at their weakest and most insecure.
"

and

http://www.washingtonpost.com/blogs/answer-sheet/wp/2013/05/15/what-if-finlands-great-teachers-taught-in-u-s-schools-not-what-you-think/
"
Among 29 wealthy countries, the United States landed second from the last in child poverty and held a similarly poor position in “child life satisfaction.” Teachers alone, regardless of how effective they are, will not be able to overcome the challenges that poor children bring with them to schools everyday.

[...]

 All teachers [in Finland] must earn a master’s degree at one of the country’s research universities. Competition to get into these teacher education programs is tough; only “the best and the brightest” are accepted. As a consequence, teaching is regarded as an esteemed profession, on par with medicine, law or engineering. There is another “teacher quality” checkpoint at graduation from School of Education in Finland. Students are not allowed to earn degrees to teach unless they demonstrate that they possess knowledge, skills and morals necessary to be a successful teacher.
But education policies in Finland concentrate more on school effectiveness than on teacher effectiveness. This indicates that what schools are expected to do is an effort of everyone in a school, working together, rather than teachers working  individually.

Lessons from high-performing school systems, including Finland, suggest that we must reconsider how we think about teaching as a profession and what is the role of the school in our society.
First, standardization should focus more on teacher education and less on teaching and learning in schools.
Second, the toxic use of accountability for schools should be abandoned.
Third, other school policies must be changed before teaching becomes attractive to more young talents. In many countries where teachers fight for their rights, their main demand is not more money but better working conditions in schools.
"

Mathematical Beauty

This week has been especially beautiful, mathematically speaking.

n-body problems are interesting and challenging.  By using the laws of gravitation and a computer and some very clever symmetry, many beautiful (and in a perfect world, stable) orbits are possible!

This set of simulations is one of the most amazing and beautiful I have ever seen. Toggle the trajectories, particularly on the last two in the list.

http://www.maths.manchester.ac.uk/~jm/Choreographies/

Biofabric is a creative way to re-imagine network diagrams. What is particularly impressive is the short animation going from the old view to the new. See the blog detailing the process here.

before

after

Visualizing sports stats is a great way to engage students with the study of mathematics! Here are some of my favorites.  

http://statmilk.com/NFL/0/? and http://www.statmilk.com/NCAAF/0/? let you visualize just about anything you would want to know about the NFL and NCAA.

http://www.chartball.com/football/ offers a creative and interesting way to visualize football games. 

I hope you enjoy these and are able to work them into your classes.  I imagine that many interesting discussions can arise from having students explore statistics with the help of these websites. 

Math & Juggling Talks & Workshops

I had the pleasure of giving a talk about the mathematics of juggling at the University of Maryland for their annual Maryland Day celebration on 27 April 2013.

Here is a short news clip.



Math and Juggling (Recut) from Matt Meiselman on Vimeo.

And here is the promo JHU CTY Online did about my work and teaching philosophy:

I will be giving several other talks and workshops this year.  A tentative schedule is below.

Workshop, Demos & Appearances ==> Summer 2013

• Sat 08 June 2013 -- Montgomery County Be Active Wellness initative 10am-2pm at the South Germantown Recreation Park next to the soccer plex.
• Mon 10 June 2013 -- Maryland School for the Deaf (Columbia) workshop + demo for 4th & 5th graders
• Sat 15 June 2013 -- Ripley's Believe it or Not + World Juggling Day the Baltimore Inner Harbor
• Sat 20 & Sun 21 July -- Artscape! 
• Sun 25 August 2013 -- Deaf Senior Association afternoon workshop + demos

If you are interested in having me give a talk and/or workshop about mathematics, juggling, or both, please feel free to contact me via twitter: @mathteacher1729 or email: mathteacher1729@yahoo.com

Is teaching math monotonous?

There was a thread on reddit.com/r/learnmath from a math undergrad who considering becoming a teacher but is worried about 'being bored with the content'. Here it is in full: "Is Teaching Math Monotonous?"

Below is my reply.

I've been tutoring my friends in math and science since I was in elementary school. I majored in math (B.S.) in 05, got my masters in teaching math (US Grades 7-12) in 06. The year of my masters, I did a full time internship teaching at a public school, then I worked as a public school teacher until spring 08. In fall 08 I started working at JHU CTY Online as an instructor, supervisor and course developer for AP Calc & College math.

I love my content and I know my content, but teaching and tutoring is not about content alone.  In my (short, limited, singular) lifetime of experience, I've found that a significant portion of the personal & professional satisfaction associated with the career of teaching & tutoring is being a facilitator of learning.  Figuring out ways to engage your students with the content, technology, and each other is key.  Knowing that the aforementioned engagement results in some struggle, eventual realizations, a sharpening of skills, and "the lightbulb going off" is a huge reason why I'm still in my field (instead of some other field making three times as much money, say).

> I'm currently an undergrad math major planning on being a teacher. I wanted to know if you math teachers out there ever find teaching math to be a monotonous task. Doesn't it get boring to teach the same material every year? 

No.  Because teaching is not all about the content.  (see comments above).

I taught algebra and geometry as a high school teacher in public schools in the USA.  I had no time to be bored because of all the other things going on in the classroom (largely discipline issues springing from the individual family circumstances of my students as well as ambient local culture). The classroom management aspect of the job was one of the main reasons I left public education.  (Awful education policy robbing the curriculum of meaning and teaching of professionalism was the other.)

I now instruct, develop and supervise online courses in AP Calc & College level math.  The content is broader and deeper than high school algebra and geometry, but it's still "just" the first one or two years of advanced undergraduate math.  The thrill of my work is working directly with my students and finding new ways to use technology to communicate mathematics.

> After a while, you must know the answer to every question before it's even asked. How does it feel to have taught the same class (say Algebra 2) for 20 years?? I'm worried that as a teacher I would feel stagnant after a few years.

I've been teaching professionally since 06, so it's hardly been 20 years, but at this stage in my career I've already reached the point where I know the kinds of topics which will be asked about over and over again.  I am still enjoying finding new ways to visualize and articulate those concepts and seeing my students go from being unfamiliar or confused to being able to understand and solve problems about those concepts.

Teaching is not all about the content.

I care about my students and wish them all the best in their endeavors.  I take great professional satisfaction in knowing that I am helping push them to their intellectual limits and get a little farther toward their ultimate goals. Reading vector calc texts for four years might get a bit dull.  Helping my students go from not knowing the subject and writing HW sets by hand to using LaTeX and advanced graphing software to create a variety of professional PDF documents full of beautiful illustrations...  That has not yet gotten dull, for me anyway.

New blog series -- 'Little known free math gems"

 "Little known free math gems"

These are tiny, free, and surprisingly powerful programs for mathematics students from algebra through college-level which can be used on virtually any laptop or desktop computer, even old ones.   

All of my screenshots will be from a laptop running Windows Vista Pro with 1.88 GHz on 1GB of RAM.

I'll be reviewing the following: I hope to do one review each week. 

1. DPGraph
2. GrafEq
3. MVT
4. Winplot
5. dfield & pplane
6. Linear

Also I plan to include:

1. screenshot techniques (cropper, mspaint)
2. useful & interesting wolframalpha commands
3. desmos
4. Geogebra resources
5. Touch Trigonometry

If you have any specific requests or know of a program I have not mentioned, please feel free to contact me. 

The many ways to plot implicit functions

There are many different ways to plot accurate and complicated implicit functions, for free and without eating up your processor.

Let's look at this implicit curve, for example:

ax^2 + bxy^3 = c  

where a, b, and c are real numbers.

In Geogebra, you can click the sliders button to create a, b, and c then type the function exactly as it appears  above in the input bar. Drag a, b, and c (or animate them if you wish by right clicking) to see the function change.

Click images to enlarge.

Create the sliders first then type the equation.

Drag the sliders to see the changes in the graph.

We can also use http://www.desmos.com to do the same thing. Desmos has the nice feature of highlighting "points of interest" (in this case, the x-intercepts are highlighted). You can also share your graph easily by clicking the blue icon at the top right and choosing your share-tool of choice.


Click images to enlarge.

Click "all" to add sliders for each variable.

Drag the sliders to see the graph change.

Share your work in a variety of ways.

And for just about any calculus course, we are done.  Geogebra and Desmos are great for polynomials but if you want to graph something like cos(xy) = c  where c is a constant you will need a different set of tools.

Gnuplot is a free, command line based, graphing program. It will not plot implicit functions by default.  It's possible to hack it by plotting a 3d function with level curves projected in the xy plane. Here is the code needed to plot cos(xy) = 1. The line "set cntrparam levels discrete 0" means "plot one contour line at z = 0".

set view 0,0
set isosamples 50,50
set contour base
set cntrparam levels discrete 0
unset surface 
set grid
unset key 
unset ztics
set xlabel "x"
set ylabel "y"
set xrange [-pi:pi]
set yrange [-pi:pi]
f(x,y) = cos(x*y)
splot f(x,y)


Click image to enlarge.

The output of the above code.

There is an easier way of doing this and here is where GrafEq, a tiny, free windows program, really shines. Just type in your function and go.


Click image to enlarge.

Here is a sampling of some of the beautiful implicit graphs you can quickly, easily, and accurately plot with this tiny little-known program.

One can also type

plot cos(x*y)=0 for x=-pi...pi, y = -pi...pi

into http://www.wolframalpha.com and obtain the following output:


Click image to enlarge.

Communicating mathematics online

How does one quickly and easily communicate upper-level mathematics entirely online?

I never interact with my students in a physical classroom. All communication happens via email, virtual meeting room (Adobe Connect), Skype, and/or phone. All of the course materials are hosted on Moodle, but I do not feel that having my students use multiple choice (or free response limited to a few characters) for all assessments is sufficient to gauge their understanding and it's certainly not sufficient to engage them in a mathematical dialogue aimed at sharpening their exploration and written communication of mathematics.  

All of the graded assessments in the AP & College math courses I supervise and instruct are free response so I can clearly see a student's thought process and offer feedback as needed. There is a great deal of material per student per course and the logistics of communicating all of this marvelous math can become overwhelming. 

Fortunately, there are two main options for students and instructors which work very well, both are illustrated below. 

1. Write work by hand, use a free app called CamScanner to send to instructor. 

• Pros
• Quick and easy -- write, scan, email. 
• Automatically color-balances & arranges images into albums (for sending an entire test at once)
• Saves to pdf, jpg, tiff, or other formats, each page ~ 200 kb 
• Very high quality image output
• Cons
• Requires an Android or iOS device, so accessibility may be an issue.
• Can be difficult or slow to edit without special software (Foxit reader is free and has nice PDF editing features) 

Example output:

CamScanner (Android | iOS ) (click to enlarge)

Detail of above (click to enlarge)

2. Use free & open-source LaTeX to typeset work. 

• Pros
• Forces students to articulate their reasoning clearly (crossing out, drawing arrows, and writing all over the page simply won't transfer.)
• Output is beautiful
• Graphics can be integrated very easily
• File size is very tiny (5 kb + images)
• Easy to edit
• Typing math becomes as natural as typing English
• Professional documents can be typed for any course, not just math!
• Learn it now instead of later!
• Cons
• Heavy up-front time investment to learn the syntax. I have a continually updated page devoted to getting students started featuring: videos, templates, and additional resources. 
• Installation of a LaTeX distribution can be tricky, but fortunately there is http://www.sharelatex.com
• Errors can be difficult to spot at first and frustrating to correct without help from an experienced user. 

Example Output: 

LaTeX (click to enlarge) download source here.

Detail of above. (click to enlarge)